Simplify the following expression: $ n = \dfrac{x}{-9x - 1} + \dfrac{-9}{2} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{x}{-9x - 1} \times \dfrac{2}{2} = \dfrac{2x}{-18x - 2} $ Multiply the second expression by $\dfrac{-9x - 1}{-9x - 1}$ $ \dfrac{-9}{2} \times \dfrac{-9x - 1}{-9x - 1} = \dfrac{81x + 9}{-18x - 2} $ Therefore $ n = \dfrac{2x}{-18x - 2} + \dfrac{81x + 9}{-18x - 2} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{2x + 81x + 9}{-18x - 2} $ $n = \dfrac{83x + 9}{-18x - 2}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{-83x - 9}{18x + 2}$